Solved Maths Questions of Matron Grade I (Main Exam)
This post contains detailed solution for Maths questions that were asked in the Kerala PSCMatron Grade I (Main Exam), which was conducted on November 08, 2024.
1.ഒരു സംഖ്യയെ 4 കൊണ്ട് ഗുണിച്ചു 10 കൂടിയപ്പോൾ 130 കിട്ടി. സംഖ്യ ഏതാണ്?
Let the x be number,4x+10 = 1304x = 130 – 104x = 120x = 120/4x = 30(5)
| Item | Detail |
|---|---|
| Given,Principal (P) = Rs. 15,000Rate (r) = 10% per annumTime (t) = 2 yearsn = 1 (no of times interest is compounded per year)A = 15,000 (1+10/100)²= 15000 (1.1)²= 15000 × 1.21= 18150To calculate the remaining amount,Remaining amount = amount after 2 years | repaid amount= 18150 – 10000= 8150Solution∴ Thomas should pay Rs. 8,150 to clear the balance of his loan.3 |
| താഴെ പറയുന്നവയിൽ സമാന്തര ശ്രേണി ഏത്?A)2-ന്റെ കൃതികളുടെ ശ്രേണിB) എണ്ണൽ സംഖ്യകളുടെ വ്യുൽക്രമത്തിന്റെ ശ്രേണിC) ഒറ്റസംഖ്യകളുടെ പകുതിയായി ഭിന്നസംഖ്യകളുടെ ശ്രേണിD) 3-ന്റെ കൃതികളുടെ ശ്രേണിExplanation:An arithmetic progression is a sequence where the difference between consecutive terms is constant.A) Sequence of powers of 2: 21, 2², 23, 24,.....2, 4, 8, 16....4 | 2. 8 – 4. 16 – 4..... the difference between them is not consistent, ∴ This is not an arithmetic progression.B) Sequence of fractions of natural numbers: 1/1, 1/2, 1/3, 1/4, ...1/2 – 1/1 = –1/2, 1/3 – 1/2 = –1/6..... the difference between them is not consistent, ∴ This is also not an arithmetic progression.C) Sequence of fractions got as half the odd numbers:Odd numbers: 1, 3, 5, 7, 9 |
| Half the Odd Numbers, ie odd nos. divided by 2: 1/2, 3/2, 5/2, 7/2,....3/2 | 1/2 = 1, 5/2 – 3/2 = 1, 7/2 – 5/2 = 1, ..... the difference between them is consistent ie, 1, ∴ This can be considered as an arithmetic progression.D) 3's Sequence of powers: 30,31, 3², 33, 34,.....1, 3, 9, 27, 81,.....3 – 1 = 2, 9 – 3 = 6, 27 – 9 = 18, ..... the difference between them is not consistent, ∴ This is also not an arithmetic progression |
| ഒരു ക്ലോക്കിലെ സമയം 7.30 ആണെങ്കിൽ മണിക്കൂർ സൂചിയും മിനിറ്റ് സൂചിയും തമ്മിലുള്ള കോണളവ് എത്ര?A) 25B) 35C) 45D) 60Explanation:Method IAngle between hour hand and minute hand =(60H | 11M)/2(for larger angle between the hour and minute hands of a clock)Angle = (60 × 7 – 11 × 30)/2Angle = 90/2Angle = 45 degrees |
| Each hour mark on a clock represents 30° (360° ÷ 12 hours).At 7 o'clock, the hour hand points at the 7.So @ 7 o'clock, the hour hand is at 7 × 30 = 210°So @ 7.30, ie, 30 minutes past 7, the hour hand has moved halfway between the 7 and 8.∴ 30° / 2 = 15°.So @ 7.30, the hour hand is at 210 + 15 = 225°Step 2: The Minute HandAt 30 minutes, the minute hand points directly at the 6 which corresponds to 6× 30 = 180°Step 3: Angle Between the HandsTo find the angle between the hands = 225° | 180°= 45°Solution∴ The angle between the hour hand and the minute hand at 7:30 is 45 degrees.10 |
Given,Principal (P) = Rs. 15,000Rate (r) = 10% per annumTime (t) = 2 yearsn = 1 (no of times interest is compounded per year)A = 15,000 (1+10/100)²= 15000 (1.1)²= 15000 × 1.21= 18150To calculate the remaining amount,Remaining amount = amount after 2 years
repaid amount= 18150 – 10000= 8150Solution∴ Thomas should pay Rs. 8,150 to clear the balance of his loan.3
താഴെ പറയുന്നവയിൽ സമാന്തര ശ്രേണി ഏത്?A)2-ന്റെ കൃതികളുടെ ശ്രേണിB) എണ്ണൽ സംഖ്യകളുടെ വ്യുൽക്രമത്തിന്റെ ശ്രേണിC) ഒറ്റസംഖ്യകളുടെ പകുതിയായി ഭിന്നസംഖ്യകളുടെ ശ്രേണിD) 3-ന്റെ കൃതികളുടെ ശ്രേണിExplanation:An arithmetic progression is a sequence where the difference between consecutive terms is constant.A) Sequence of powers of 2: 21, 2², 23, 24,.....2, 4, 8, 16....4
2. 8 – 4. 16 – 4..... the difference between them is not consistent, ∴ This is not an arithmetic progression.B) Sequence of fractions of natural numbers: 1/1, 1/2, 1/3, 1/4, ...1/2 – 1/1 = –1/2, 1/3 – 1/2 = –1/6..... the difference between them is not consistent, ∴ This is also not an arithmetic progression.C) Sequence of fractions got as half the odd numbers:Odd numbers: 1, 3, 5, 7, 9
Half the Odd Numbers, ie odd nos. divided by 2: 1/2, 3/2, 5/2, 7/2,....3/2
1/2 = 1, 5/2 – 3/2 = 1, 7/2 – 5/2 = 1, ..... the difference between them is consistent ie, 1, ∴ This can be considered as an arithmetic progression.D) 3's Sequence of powers: 30,31, 3², 33, 34,.....1, 3, 9, 27, 81,.....3 – 1 = 2, 9 – 3 = 6, 27 – 9 = 18, ..... the difference between them is not consistent, ∴ This is also not an arithmetic progression
ഒരു ക്ലോക്കിലെ സമയം 7.30 ആണെങ്കിൽ മണിക്കൂർ സൂചിയും മിനിറ്റ് സൂചിയും തമ്മിലുള്ള കോണളവ് എത്ര?A) 25B) 35C) 45D) 60Explanation:Method IAngle between hour hand and minute hand =(60H
11M)/2(for larger angle between the hour and minute hands of a clock)Angle = (60 × 7 – 11 × 30)/2Angle = 90/2Angle = 45 degrees
Each hour mark on a clock represents 30° (360° ÷ 12 hours).At 7 o'clock, the hour hand points at the 7.So @ 7 o'clock, the hour hand is at 7 × 30 = 210°So @ 7.30, ie, 30 minutes past 7, the hour hand has moved halfway between the 7 and 8.∴ 30° / 2 = 15°.So @ 7.30, the hour hand is at 210 + 15 = 225°Step 2: The Minute HandAt 30 minutes, the minute hand points directly at the 6 which corresponds to 6× 30 = 180°Step 3: Angle Between the HandsTo find the angle between the hands = 225°
180°= 45°Solution∴ The angle between the hour hand and the minute hand at 7:30 is 45 degrees.10